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Soil slope stability analysis combining shear strength reduction and slip line method. Supervisor: Yongchang Cai Ph.D. candidate: Jie Wu School of Civil Engineering Tongji University, China. Research background. - PowerPoint PPT Presentation
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Soil slope stability analysis combining shear strength reduction and slip line method
Supervisor: Yongchang Cai
Ph.D. candidate: Jie Wu
School of Civil Engineering
Tongji University, China
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Research background
Predicting the stability of soil slopes is a classical problem for
both of practicing engineers and academics.
Picture from: http://www.ccma.vic.gov.au/soilhealth/photos.htm
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Two main challenges need to be confronted when
dealing with soil slope
Research background
1. The Determination of potential slip lines of the soil slope
2. The calculation of corresponding safety factors
Picture from: http://ceae.colorado.edu/~regueiro/images/slope.jpg
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Research background
When the limit equilibrium method is applied
1
3
The stress strain behavior of soil are often neglected
The calculation models are often overly simplified
Arbitrary assumptions are usually introduced to ensure static determinacy
1
22
3
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Research background
In the past several decades, there have been growing interests
in Numerical slip line theory, which is developed from the
classical slip line theory. As a particular method for soil slope
stability analysis, the potential slip line surfaces can be tracked
in an efficient way.
Slip line
Start points of the search
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Content
Slip line method for evaluating slope stability
Application in soil slope stability analysis
Combination of Shear strength reduction and slip line method
Conclusion
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Slip line method for evaluating slope stability
7
For plane problem, when failure occurs, it has two failure planes(lines) and the angle μ between the failure plane(line) and the principal stress orientation is specific. As shown in figure below, 1 and 2 represents the maximum principal stress orientation(θ) and the minimum principal stress orientation, respectively. And α and β represent two failure planes(lines).
Traditional Slip line theory
tan( )
tan( )
dyu
dxdy
udx
:
:
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Slip line method for evaluating slope stability
Traditional Slip line theory
M-C material Tresca material
For M-C material:
For Tresca material:
However, Traditional Slip line theory is based on rigid-plastic assumption and it can only solve some simple problems.
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Slip line method for evaluating slope stability
Numerical Slip line theory
2 2
2 2
cos sin 2 sin cos( )sin cos (cos sin )
n y x xy
n y x xy
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Slip line method for evaluating slope stability
0n
1
1
21 = arctan
2
21 = arctan +90
2
xyx y
x y
xyy x
x y
when
when
,
,
2 23 1
3 1
cos sin( )sin cos
n
n
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Slip line method for evaluating slope stability
2 21 3
3 1
( sin cos ) tan
( )sin cos
cK
So, the slope safety can be defined as below:
For the minimum of K, solve the equation 0K
3 1
3 1
(45 arcsin( ))2 *cotc
Thus, the two surfaces of the smallest anti-shear safety factor can be expressed as:
3 1
3 1
(45 arcsin( ))2 *cotc
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Slip line method for evaluating slope stability
By linking the critical slip surface of each point, the slip surface group of slopes can be obtained. The safety factors of the slip surfaces can be calculated by the formula below. The slip surface corresponding to the minimum safety factor is the critical slip surface of slopes stability.
1
1
tann
ij ij ij ijj
n
ij ijj
c l
Fl
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Application in soil slope stability analysis
The following is the procedure of slip line theory to analyze soil slopes stability, that is, the stress distribution and its value in soil slopes is calculated by Ansys and then the slip line theory is applied to find the potential slip surface based on the stress status of the slopes.
1
Modeling in Ansys
2 3
Stress distribution in slopes
4critical slip
surface and safety
factor
Searching the
potential slip line surfaces
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Example 1
This example was provided by Australian Computer Aided Design Society (Donald and Giam, 1992).
Safety factor=1
Geometric model
Finite element mesh
γ( KN/
m3)E( Kp
a)μ c( KPa
)Ψ(°)
25 1e7 0.2 1e3 38
Reference calculation result:
In Limit Equilibrium State
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Example 1 (cont.)
Contours of maximum principal stress (Elasticity)
Critical slip surfaces (Elastoplastic)
Contours of maximum principal stress (Elastoplastic)
Critical slip surfaces (Elasticity)
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Orientation of slip line (Elastoplastic)
Example 1 (cont.)
Orientation of slip line (Elasticity)
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Plastic range indicated in red color
material γ/KN m-3 c/KPa Ψ/° E/KPa v
Layer 1 19.5 0 38.0 1.0*104 0.25
Layer 2 19.5 5.3 23.0 1.0*104 0.25
Layer 3 19.5 7.2 20.0 1.0*104 0.25Layer 1
Layer 2
Layer 3 Reference safety factor is 1.400
Example 2
Another benchmark from Australian Computer Aided Design Society
The orientation of slip line
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Example 2 (cont.)
Shear strength reduction method, Fs=1.450
Limit equilibrium method, Fs=1.400
Critical slip surface, Fs=1.487
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Application in soil slope stability analysis
Based on the calculation results of the 2 examples, some conclusions can be drawn as follows:
When the soil slope, especially its top area, is not in the plastic state, there is a dramatic change of the orientation of the slip line and the slip surface tracked is singular at corresponding area, and the factor of safety is also not minimum.
1. The shear strength reduction method can be employed to reduce the material parameters until materials of the slope approaching the plastic state. Then the slip surface calculated maybe not singular and would be more like the real one.
2. the defect that the slip surface cannot be easily obtained by the conventional shear strength reduction method can also be corrected.
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Combination of shear strength reduction and slip line method
The central concept of the SSR method is very simple. Successively reduce some factors in the shear strengths of slope materials until the finite element model does not converge to a solution, which means the failure occurs. The critical factor at which failure occurs is taken to be the factor of safety.
The following is the combination of the shear strength reduction and slip line method.
1
Modeling in Ansys
3 4
Stress distribution in slopes
5Comparing the shape
of different slip
surfaces
Searching the critical
slip surfaces
2Set a range of different
strength reduction
factors
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Combination of shear strength reduction and slip line method
Plastic range indicated in red color, strength reduction factor is 1.3
The critical slip line, safety factor is 1.073
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Combination of shear strength reduction and slip line method
Plastic range indicated in red color, strength reduction factor is 1.4
The critical slip line, safety factor is 1.008
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Combination of shear strength reduction and slip line method
Plastic range indicated in red color, strength reduction factor is 1.45
The critical slip line, safety factor is 0.997
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Conclusions
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· The slip surface is singular and not as smooth as the real one if
the material, particularly in the top of the slope, is in elastic
state rather than plastic state.
· The slip line method is time efficient and no priori assumptions have
to be made when it is employed to the stability analyze of the soil
slope.
· The combination of strength reduction and slip line method can
correct the defect that the slip surface can not be directly get by the
strength reduction method, and is an effective way to track the slip
surfaces and to evaluate soil slopes stability.
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Thank you very much for your
attention !
AcknowledgementsThe authors gratefully acknowledge the support of national science and technology support program (2011BAB08B01), and program for new century excellent talents of ministry of education of China (NCET-12-0415).